Minersville Area School District



Minersville Area Curriculum Mapping 2019-2020Eighth Grade Math - SpottsMonthContentSkillsAssessmentStandardsConceptsSeptemberIntegers and Rational Numbers*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math* Adding, subtracting, multiplying and dividing integers*Square and cube roots*Order of Operations*Real world applicationPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.1.7.E.1MO7.A-N.1.1.1MO7.A-N.1.1.3CC.2.2.8.B.1MO8.B-E.1.1.2CC.2.1.8.E.1MO8.B-E.1.1.1MO8.B-E.1.1.3MO8.B-E.1.1.4*Apply and extend previous understandings of operations with fractions to operations with rational numbers*Apply properties to operations to add and subtract rational numbers, including real world context* Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats* Apply concepts of radicals and integer exponents to generate equivalent expressions. *Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator. Example: If x^2 = 25 then x = ±√25.*Distinguish between rational and irrational numbers using their properties. * Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).* Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2.* Use rational approximations of irrational numbers to compare and order irrational numbers.September and OctoberExponent Properties*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math*Multiplication properties*Division properties*Power to a Power Properties*Negative and Zero Properties*Scientific Notation-Convert from scientific to standard form-Convert from standard to scientific form-Multiply and divide scientific notation*Real World AppPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.1.8.E.1MO8.B-E.1.1.1MO8.B-E.1.1.3MO8.B-E.1.1.4* Distinguish between rational and irrational numbers using their properties. * Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).* Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2.* Use rational approximations of irrational numbers to compare and order irrational numbers.OctoberIrrational Numbers*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math* Estimate Square roots and cube roots*Number Line*Operations with roots*Square/Cube root equationsPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsCC.2.1.8.E.4MO8.B-E.1.1.5MO8.B-E.1.1.3MO8.B-E.1.1.4* Estimate irrational numbers by comparing them to rational numbers. *Locate/identify rational and irrational numbers at their approximate locations on a number line.* Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2.* Use rational approximations of irrational numbers to compare and order irrational numbers.NovemberBasic Algebra*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math* Solving one step equations* Solving two step equationsSolving multi-step equations*One solution, No solution, infinite solutions* Real World AppPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.2.8.3.BMO8.B-E.1.1.1MO8.B-E.1.1.2*Analyze and solve linear equations and pairs of simultaneous linear equations. *Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: 3^12 x 3^-15 = 3^-3 = 1/(3^3) * Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.DecemberPythag. Theorem*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math* Parts of a Right Triangle*Prove Right Triangle*Solve Missing Side*Distance*Complex Figures Using Right Triangle*3D Shapes*Real World Application. Paper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.3.8.A.3MO8.C-G.2.1.1MO8.C-G.2.1.2MO8.C-G.2.1.3* Understand and apply the Pythagorean Theorem to solve problems. * Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.* Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)* Apply the Pythagorean theorem to find the distance between two points in a coordinate system.December and JanuaryFunctions*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math*Function or Not*X-Y Function Tables*Functions to a Graph*Rate of Change*Slope*Writing the Function Rule*Graphing Lines*Comparing Slope/ Rate of change*Real World ApplicationPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.2.8.B.2MO8.B-E.2.1.1MO8.B-E.2.1.2MO8.B-E.2.1.3MO8.B-F.1.1.1MO8.B-F.1.1.2MO8.B-F.1.1.3CC.2.2.8.C.1CC.2.2.8.C.2MO8.B-F.2.1.1MO8.B-F.2.1.2* Understand the connections between proportional relationships, lines, and linear equations. *Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.*Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.*Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.*Define, evaluate, and compare functions. *Use concepts of functions to model relationships between quantities. *Represent or interpret functional relationships between quantities using tables, graphs, and descriptions.*Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally.FebruarySystems*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math*Slope Intercept Form*Slope and y – intercept*Graphing Lines from Equations*Write equations using graphs* Rewriting equations into Slope Intercept form*Solving systems by graphing*Solving Systems by Substitution*Real World ApplicationPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzes CC.2.2.HS.D.7CC.2.2.HS.D.10CC.2.2.8.B.2MO8.B-E.2.1.3CC.2.2.8.B.3MO8.B-E.3.1.3MO8.B-E.3.1.4MO8.B-E.3.1.5* Understand the connections between proportional relationships, lines, and linear equations. *Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.*Analyze and solve linear equations and pairs of simultaneous linear equations. *Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.*Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.*Solve real-world and mathematical problems leading to two linear equations in two variables. Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.MarchStatistics*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math*Linear Vs. Nonlinear*Scatter Plots*Linear Regression*Two Way Tables*Relative FrequencyPaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzes*CC.2.4.8.B.1*MO8.D-S.1.1.1*MO8.D-S.1.1.2*MO8.D-S.1.1.3*CC.2.4.8.B.2*MO8.D-S.1.2.1* Analyze and/or interpret bivariate data displayed in multiple representations. *Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative correlation, linear association, and nonlinear association.*For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line.*Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Example: In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.*Understand that patterns of association can be seen in bivariate data utilizing frequencies. *Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible associations between the two variables. Example: Given data on whether students have a curfew on school nights and whether they have assigned chores at home, is there evidence that those who have a curfew also tend to have chores?AprilVolume*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources*Get More Math*Volume of- Cube- Rectangular Prism- Cone- Cylinders- SpherePaper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.3.8.A.1MO8.C-G.3.1.1* Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems. *Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.May and JuneTrans-formations and inequalities*Textbook*Internet Resources*Self-Created Resources*Common Core Resources*SAS Website Resources*Workbook Resources *Get More Math*Reflections - Slope of the Reflection Line*Translations*Rotations*Dilations*Graph Inequalities*Graph Compound Inequalities*Solve Linear Inequalities*Graph Linear Inequalities Paper/Pencil TestsHomeworkClassroom ObservationOpen Ended PromptsIndividual/ Group ProjectsQuizzesCC.2.3.8.A.2MO8.C-G.1.1.1MO8.C-G.1.1.2MO8.C-G.1.1.3MO8.C-G.1.1.4CC.2.2.7.B.3MO7.B-E.2.2.1CC.2.2.8.B.3MO8.B-E.3.1.1MO8.B-E.3.1.2*Understand and apply congruence, similarity, and geometric transformations using various tools.*Identify and apply properties of rotations, reflections, and translations. Example: Angle measures are preserved in rotations, reflections, and translations.*Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.*Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.*Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.*Analyze and solve linear equations and pairs of simultaneous linear equations. *Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).*Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.Developed by Shane M. Spotts ................
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